A heat sink is a term for a component or assembly that transfers heat generated within a solid material to a fluid or gas medium, such as air or a liquid. A heat sink is typically designed to increase the surface area in contact with the cooling fluid or gas surrounding it, such as the air. Approach air velocity, choice of material, fin (or other protrusion) design and surface treatment are some of the design factors which influence the thermal resistance, i.e. thermal performance, of a heat sink. See, en.wikipedia.org/wiki/Heat_sink.
Heatsinks operate by removing heat from an object to be cooled into the surrounding air, gas or liquid through convection and radiation. Convection occurs when heat is either carried passively from one point to another by fluid motion (forced convection) or when heat itself causes fluid motion (free convection). When forced convection and free convection occur together, the process is termed mixed convection. Radiation occurs when energy, for example in the form of heat, travels through a medium or through space and is ultimately absorbed by another body. Thermal radiation is the process by which the surface of an object radiates its thermal energy in the form of electromagnetic waves. Infrared radiation from a common household radiator or electric heater is an example of thermal radiation, as is the heat and light (IR and visible EM waves) emitted by a glowing incandescent light bulb. Thermal radiation is generated when heat from the movement of charged particles within atoms is converted to electromagnetic radiation.
A heatsink tends to decrease the maximum temperature of the exposed surface, because the power is transferred to a larger volume. This leads to a possibility of diminishing return on larger heatsinks, since the radiative and convective dissipation tends to be related to the temperature differential between the heatsink surface and the external medium. Therefore, if the heatsink is oversized, the efficiency of heat shedding is poor. If the heatsink is undersized, the object may be insufficiently cooled, the surface of the heatsink dangerously hot, and the heat shedding not much greater than the object itself absent the heatsink.
A heat sink transfers thermal energy from a higher temperature to a lower temperature fluid or gas medium, by a process such as radiation, convection, and diffusion. The fluid medium is frequently air, but can also be water or in the case of heat exchangers, oil, and refrigerants. Fourier's law of heat conduction, simplified to a one-dimensional form in the direction x, shows that when there is a temperature gradient in a body, heat will be transferred from the higher temperature region to the lower temperature region. The rate at which heat is transferred by conduction, qk, is proportional to the product of the temperature gradient and the cross-sectional area through which heat is transferred:
                              q          k                =                  kA          ⁢                                    d              ⁢                                                          ⁢              T                                      d              ⁢                                                          ⁢              x                                                          (        1        )            
where qk is the rate of conduction, k is a constant which depends on the heat-conducting material, A is the surface area through which the heat is conducted, and dT/dx is the temperature gradient, i.e., the rate of change of temperature with respect to distance (for simplicity, the equation is written in one dimension). Thus, according to Fourier's law (which is not the only consideration by any means), heatsinks benefit from having a large surface area exposed to the medium into which the heat is to be transferred.
Consider a heat sink in a duct, where air flows through the duct, and the heat sink base is higher in temperature than the air. Assuming conservation of energy, for steady-state conditions, and applying the convection-cooling law, also known as the Newton's law of cooling, gives the following set of equations.
                              Q          .                =                              m            .                    ⁢                                    c                              p                ,                in                                      ⁡                          (                                                T                                      air                    ,                    out                                                  -                                  T                                      air                    ,                    in                                                              )                                                          (        2        )                                                      Q            .                    =                                                    T                hs                            -                              T                                  air                  ,                  av                                                                    R              hs                                      ⁢                                  ⁢        where                            (        3        )                                          T                      air            ,            av                          =                                            T                              air                ,                out                                      +                          T                              air                ,                in                                              2                                    (        4        )            
and {dot over (Q)} is the first derivative of the thermal energy over time—
      Q    .    =                    d        ⁢                                  ⁢        Q                    d        ⁢                                  ⁢        t              .  
Using the mean air temperature is an assumption that is valid for relatively short heat sinks. When compact heat exchangers are calculated, the logarithmic mean air temperature is used. {dot over (m)} is the first derivative of mass over time, i.e., the air mass flow rate in kg/s.
The above equations show that when the airflow through or around the heat sink decreases, this results in an increase in the average air temperature. This in turn increases the heat sink base temperature. And additionally, the thermal resistance of the heat sink will also increase. The net result is a higher heat sink base temperature. The inlet air temperature relates strongly with the heat sink base temperature. Therefore, if there is no air or fluid flow around the heat sink, the energy dissipated to the air cannot be transferred to the ambient air. Therefore, the heat sink functions poorly.
Other examples of situations, in which a heat sink has impaired efficiency: (a) pin fins have a lot of surface area, but the pins are so close together that air has a hard time flowing through them; (b) aligning a heat sink so that the fins are not in the direction of flow; (c) aligning the fins horizontally for a natural convection heat sink. Whilst a heat sink is stationary and there are no centrifugal forces and artificial gravity, air that is warmer than the ambient temperature always flows upward, given essentially-still-air surroundings; this is convective cooling.
The most common heat sink material is aluminum. Chemically pure aluminum is not used in the manufacture of heat sinks, but rather aluminum alloys. Aluminum alloy 1050A has one of the higher thermal conductivity values at 229 W/m·K. However, it is not recommended for machining, since it is a relatively soft material. Aluminum alloys 6061 and 6063 are the more commonly used aluminum alloys, with thermal conductivity values of 166 and 201 W/m·K, respectively. The aforementioned values are dependent on the temper of the alloy.
Copper is also used since it has around twice the conductivity of aluminum, but is three times as heavy as aluminum. Copper is also around four to six times more expensive than aluminum, but this is market dependent. Aluminum has the added advantage that it is able to be extruded, while copper cannot. Copper heat sinks are machined and skived. Another method of manufacture is to solder the fins into the heat sink base.
Another heat sink material that can be used is diamond. With a thermal conductivity value of 2000 W/m·K, it exceeds that of copper by a factor of five. In contrast to metals, where heat is conducted by delocalized electrons, lattice vibrations are responsible for diamond's very high thermal conductivity. For thermal management applications, the outstanding thermal conductivity and diffusivity of diamond are essential. CVD diamond may be used as a sub-mount for high-power integrated circuits and laser diodes.
Composite materials also can be used. Examples are a copper-tungsten pseudoalloy, AlSiC (silicon carbide in aluminum matrix), Dymalloy (diamond in copper-silver alloy matrix), and E-Material (beryllium oxide in beryllium matrix). Such materials are often used as substrates for chips, as their thermal expansion coefficient can be matched to ceramics and semiconductors.
Fin efficiency is one of the parameters which make a higher thermal conductivity material important. A fin of a heat sink may be considered to be a flat plate with heat flowing in one end and being dissipated into the surrounding fluid as it travels to the other. As heat flows through the fin, the combination of the thermal resistance of the heat sink impeding the flow and the heat lost due to convection, the temperature of the fin and, therefore, the heat transfer to the fluid, will decrease from the base to the end of the fin. This factor is called the fin efficiency and is defined as the actual heat transferred by the fin, divided by the heat transfer were the fin to be isothermal (hypothetically the fin having infinite thermal conductivity). Equations 5 and 6 are applicable for straight fins.
                              η          f                =                              tanh            ⁡                          (                              mL                c                            )                                            mL            c                                              (        5        )                                          mL          c                =                                                            2                ⁢                                                                  ⁢                                  h                  f                                                            kt                f                                      ⁢                          L              f                                                          (        6        )            
Where:                hf is the convection coefficient of the fin                    Air: 10 to 100 W/(m2·K)            Water: 500 to 10,000 W/(m2·K)                        k is the thermal conductivity of the fin material                    Aluminum: 120 to 240 W/(m2·K)                        Lf is the fin height (m)        tf is the fin thickness (m)        
Another parameter that concerns the thermal conductivity of the heat sink material is spreading resistance. Spreading resistance occurs when thermal energy is transferred from a small area to a larger area in a substance with finite thermal conductivity. In a heat sink, this means that heat does not distribute uniformly through the heat sink base. The spreading resistance phenomenon is shown by how the heat travels from the heat source location and causes a large temperature gradient between the heat source and the edges of the heat sink. This means that some fins are at a lower temperature than if the heat source were uniform across the base of the heat sink. This non-uniformity increases the heat sink's effective thermal resistance.
A pin fin heat sink is a heat sink that has pins that extend from its base. The pins can be, for example, cylindrical, elliptical or square/geometric polygonal. A second type of heat sink fin arrangement is the straight fin. These run the entire length of the heat sink. A variation on the straight fin heat sink is a cross cut heat sink. A straight fin heat sink is cut at regular intervals but at a coarser pitch than a pin fin type.
In general, the more surface area a heat sink has, the better it works. However, this is not always true. The concept of a pin fin heat sink is to try to pack as much surface area into a given volume as possible. As well, it works well in any orientation. Kordyban has compared the performance of a pin fin and a straight fin heat sink of similar dimensions. Although the pin fin has 194 cm2 surface area while the straight fin has 58 cm2, the temperature difference between the heat sink base and the ambient air for the pin fin is 50° C. For the straight fin it was 44° C. or 6° C. better than the pin fin. Pin fin heat sink performance is significantly better than straight fins when used in their intended application where the fluid flows axially along the pins rather than only tangentially across the pins. See, Kordyban, T., Hot air rises and heat sinks—Everything you know about cooling electronics is wrong, ASME Press, NY 1998.
Another configuration is the flared fin heat sink; its fins are not parallel to each other, but rather diverge with increasing distance from the base. Flaring the fins decreases flow resistance and makes more air go through the heat sink fin channel; otherwise, more air would bypass the fins. Slanting them keeps the overall dimensions the same, but offers longer fins. Forghan, et al. have published data on tests conducted on pin fin, straight fin and flared fin heat sinks. See, Forghan, F., Goldthwaite, D., Ulinski, M., Metghalchi, M., Experimental and Theoretical Investigation of Thermal Performance of Heat Sinks, ISME, May. 2001. They found that for low approach air velocity, typically around 1 m/s, the thermal performance is at least 20% better than straight fin heat sinks. Lasance and Eggink also found that for the bypass configurations that they tested, the flared heat sink performed better than the other heat sinks tested. See, Lasance, C. J. M and Eggink, H.J., A Method to Rank Heat Sinks in Practice: The Heat Sink Performance Tester, 21st IEEE SEMI-THERM Symposium 2001.
The heat transfer from the heatsink is mediated by two effects: conduction via the coolant, and thermal radiation. The surface of the heatsink influences its emissivity; shiny metal absorbs and radiates only a small amount of heat, while matte black is a good radiator. In coolant-mediated heat transfer, the contribution of radiation is generally small. A layer of coating on the heatsink can then be counterproductive, as its thermal resistance can impair heat flow from the fins to the coolant. Finned heatsinks with convective or forced flow will not benefit significantly from being colored. In situations with significant contribution of radiative cooling, e.g. in case of a flat non-finned panel acting as a heatsink with low airflow, the heatsink surface finish can play an important role. Matte-black surfaces will radiate much more efficiently than shiny bare metal. The importance of radiative vs. coolant-mediated heat transfer increases in situations with low ambient air pressure (e.g. high-altitude operations) or in vacuum (e.g. satellites in space).    Fourier, J. B., 1822, Theorie analytique de la chaleur, Paris; Freeman, A., 1955, translation, Dover Publications, Inc, NY.    Kordyban, T., 1998, Hot air rises and heat sinks—Everything you know about cooling electronics is wrong, ASME Press, NY.    Anon, Unknown, “Heat sink selection”, Mechanical engineering department, San Jose State University [27 Jan. 2010]. www.engr.sjsu.edu/ndejong/ME%20146%20files/Heat%20Sink.pptwww.engr.sjsu.edu/ndejong/ME%20146%20files/Heat%20Sink.ppt    Sergent, J. and Krum, A., 1998, Thermal management handbook for electronic assemblies, First Edition, McGraw-Hill.    Incropera, F. P. and DeWitt, D. P., 1985, Introduction to heat transfer, John Wiley and sons, NY.    Forghan, F., Goldthwaite, D., Ulinski, M., Metghalchi, M., 2001, Experimental and Theoretical Investigation of Thermal Performance of Heat Sinks, ISME May.    Lasance, C. J. M and Eggink, H. J., 2001, A Method to Rank Heat Sinks in Practice: The Heat Sink Performance Tester, 21st IEEE SEMI-THERM Symposium.    ludens.cl/Electron/Thermal.html    Lienard, J. H., IV & V, 2004, A Heat Transfer Textbook, Third edition, MIT    Saint-Gobain, 2004, “Thermal management solutions for electronic equipment” 22 Jul. 2008 www.fff.saint-gobain.com/Media/Documents/S0000000000000001036/ThermaCool%20Brochure.pdf    Jeggels, Y. U., Dobson, R. T., Jeggels, D. H., Comparison of the cooling performance between heat pipe and aluminium conductors for electronic equipment enclosures, Proceedings of the 14th International Heat Pipe Conference, Florianópolis, Brazil, 2007.    Prstic, S., Iyengar, M., and Bar-Cohen, A., 2000, Bypass effect in high performance heat sinks, Proceedings of the International Thermal Science Seminar Bled, Slovenia, June 11-14.    Mills, A. F., 1999, Heat transfer, Second edition, Prentice Hall.    Potter, C. M. and Wiggert, D. C., 2002, Mechanics of fluid, Third Edition, Brooks/Cole.    White, F. M., 1999, Fluid mechanics, Fourth edition, McGraw-Hill International.    Azar, A, et al., 2009, “Heat sink testing methods and common oversights”, Qpedia Thermal E-Magazine, January 2009 Issue. www.qats.com/cpanel/UploadedPdf/January20092.pdf
Several structurally complex heatsink designs are discussed in Hernon, US App. 2009/0321045, incorporated herein by reference.
The relationship between friction and convention in heatsinks is discussed by Frigus Primore in “A Method for Comparing Heat Sinks Based on Reynolds Analogy,” available at www.frigprim.com/downloads/Reynolds_analogy_heatsinks.PDF, last accessed Apr. 28, 2010. This article notes that for, plates, parallel plates, and cylinders to be cooled, it is necessary for the velocity of the surrounding fluid to be low in order to minimize mechanical power losses. However, larger surface flow velocities will increase the heat transfer efficiency, especially where the flow near the surface is turbulent, and substantially disrupts a stagnant surface boundary layer. Primore also discusses heatsink fin shapes and notes that no fin shape offers any heat dissipation or weight advantage compared with planar fins, and that straight fins minimize pressure losses while maximizing heat flow. Therefore, the art generally teaches that generally flat and planar surfaces are appropriate for most heatsinks.
Frigus Primore, “Natural Convection and Inclined Parallel Plates,” www.frigprim.com/articels2/parallel_pl_Inc.html, last accessed Apr. 29, 2010, discusses the use of natural convection (i.e., convection due to the thermal expansion of a gas surrounding a solid heatsink in normal operating conditions) to cool electronics. One of the design goals of various heatsinks is to increase the rate of natural convection. Primore suggests using parallel plates to attain this result. Once again, Primore notes that parallel plate heat sinks are the most efficient and attempts to define the optimal spacing and angle (relative to the direction of the fluid flow) of the heat sinks according to the equations in FIG. 1.
In another article titled “Natural Convection and Chimneys,” available at www.frigprim.com/articels2/parallel_plchim.html, last accessed Apr. 29, 2010, Frigus Primore discusses the use of parallel plates in chimney heat sinks. One purpose of this type of design is to combine more efficient natural convection with a chimney. Primore notes that the design suffers if there is laminar flow (which creates a re-circulation region in the fluid outlet, thereby completely eliminating the benefit of the chimney) but benefits if there is turbulent flow which allows heat to travel from the parallel plates into the chimney and surrounding fluid.
Batten, Paul, et al. “Sub-Grid Turbulence Modeling for Unsteady Flow with Acoustic Resonance,” available at www.metacomptech.com/cfd++/00-0473.pdf, last accessed Apr. 29, 2010, expressly incorporated herein by reference, discuss that when a fluid is flowing around an obstacle, localized geometric features, such as concave regions or cavities, create pockets of separated flow which can generate self-sustaining oscillations and acoustic resonance. The concave regions or cavities serve to substantially reduce narrow band acoustic resonance as compared to flat surfaces. This is beneficial to a heat sink in a turbulent flow environment because it allows for the reduction of oscillations and acoustic resonance, and therefore for an increase in the energy available for heat transfer.
Liu, S., et al., “Heat Transfer and Pressure Drop in Fractal Microchannel Heat Sink for Cooling of Electronic Chips,” 44 Heat Mass Transfer 221 (2007), discuss a heatsink with a “fractal-like branching flow network.” Liu's heatsink includes channels through which fluids would flow in order to exchange heat with the heatsink.
Y. J. Lee, “Enhanced Microchannel Heat Sinks Using Oblique Fins,” IPACK 2009-89059, similarly discusses a heat sink comprising a “fractal-shaped microchannel based on the fractal pattern of mammalian circulatory and respiratory system.” Lee's idea, similar to that of Liu, is that there would be channels inside the heatsink through which a fluid could flow to exchange heat with the heatsink. The stated improvement in Lee's heatsink is (1) the disruption of the thermal boundary layer development; and (2) the generation of secondary flows.
Pence, D. V., 2002, “Reduced Pumping Power and Wall Temperature in Microchannel Heat Sinks with Fractal-like Branching Channel Networks”, Microscale Thermophys. Eng. 5, pp. 293-311, mentions heatsinks that have fractal-like channels allowing fluid to enter into the heat sink. The described advantage of Pence's structure is increased exposure of the heat sink to the fluid and lower pressure drops of the fluid while in the heatsink.
In general, a properly designed heatsink system will take advantage of thermally induced convection or forced air (e.g., a fan). In general, a turbulent flow near the surface of the heatsink disturbs a stagnant surface layer, and improves performance. In many cases, the heatsink operates in a non-ideal environment subject to dust or oil; therefore, the heatsink design must accommodate the typical operating conditions, in addition to the as-manufactured state.
Therefore, two factors appear to conflict in optimizing the configuration of an external: the surface configuration designed to disturb laminar flow patterns, create turbulence, and enhance convective heat transfer, and the desire to efficiently flow large volumes of heat transfer fluid (e.g., air), over the surfaces, which is enhanced by laminar (smooth) flow. Even in passive dissipative device, convective flow may be a significant factor, and reducing air flow volume and velocity by increasing the effective impedance can be counterproductive. On the other hand, in some cases, the amount of energy necessary to move the air is dwarfed by the problem to be solved. In many computing systems, the processors are thermally constrained, that is, the functioning of the processor is limited by the ability to shed heat. In such cases, innovative ways to improve the efficiency of heat transfer may yield significant benefit, even if in some regimes of operation they impose certain inefficiencies.
Prior art heatsink designs have traditionally concentrated on geometry that is Euclidian, involving structures such as the pin fins, straight fins, and flares discussed above.    N J Ryan, D A Stone, “Application of the FD-TD method to modelling the electromagnetic radiation from heatsinks”, IEEE International Conference on Electromagnetic Compatibility, 1997. 10th (1-3 Sep. 1997), pp: 119-124, discloses a fractal antenna which also serves as a heatsink in a radio frequency transmitter.    Lance Covert, Jenshan Lin, Dan Janning, Thomas Dalrymple, “5.8 GHz orientation-specific extruded-fin heatsink antennas for 3D RF system integration”, 23 Apr. 2008 DOI: 10.1002/mop.23478, Microwave and Optical Technology Letters Volume 50, Issue 7, pages 1826-1831, July 2008 also provide a heatsink which can be used as an antenna.